Bôcher theorem

Bôcher's theorem

In mathematics, Bôcher's theorem, named after Maxime Bôcher, states that the finite zeros of the derivative r'(z) of a nonconstant rational function r(z) that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of r(z) and particles of negative mass at the poles of r(z) , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.